Answer
$d=30cm$
Work Step by Step
The distance between beetle and scorpion is related to transverse and longitudinal speed $'v_t'$ and $'v_l'$.
Mathematically, $d=v_tt_t=v_lt_t$
$t_t$ and $t_l$ represent arrival times of transverse and longitudinal waves
from the above equation, we can derive the following result
$\frac{t_t}{t_l}=\frac{v_l}{v_t}$
$\frac{t_t}{t_l}=\frac{150}{50}=3$
or $t_t=3t_l$
given that $\Delta{t}=4{ms}=4\times10^{-3}s$
but $\Delta{t}=t_t-t_l$
put $t_t=3t_l$
$\Delta{t}=3t_l-t_l=2t_l=4\times10^{-3}$
$t_l=\frac{4}{2}\times10^{-3}=2\times10^{-3}$
Now from the very first equation, we have
$d=v_lt_l$
Put the values
$d=(150)(2\times10^{-3})=0.30m=30cm$
$d=30cm$
